Since prehistoric times, mankind has used instrument tools to perform certain tasks that would not be possible or very difficult to do--or at very least an inferior result would be produced--without tools. Such tools include tools for cutting, shaping, folding, measuring, and so on. Tools are typically designed to make a particular job more easy, and more expedient than if the tool was not used, and very often the task at hand is performed better as a result of using a proper tool. Over many centuries, tools have evolved so as to provide better ways to perform tasks than would be possible without tools. Indeed, not only can tools provide better ways of performing tasks, they can help achieve better results. They may even be able to provide results in situations where useful results could not be achieved without tools.
One very important function that a tool can perform is that of combining operations in a manner that simplifies the realization of an end result. Such a tool may indeed combine two functions into one tool, such as holding and shaping an object, or holding and measuring an object. In either of these cases, the tool is performing a function that might otherwise be done by more than one tool or by tool and possibly by a person's hand. Ultimately, the end result of shaping, measuring, or whatever, is or easily and accurately achieved through use of a tool that provides multiple functions.
Indeed, some tools perform functions that simply can not be achieved without the use of that tool, or at least some similar tool. One subject sample of this kind of tool is a measuring device, whether it be for measuring linear distances, angles, or even something more complicated such as rates of flow, sound pressure level, illumination, and so on.
For the simple matter of measuring distances, it is not possible to accurately measure a distance without some sort of scale. A scale provides a reference, wherein a basic unit of reference is determined and a contiguous series of such units is used to form the scale. Such a scale can be found on a simple common ruler, tape measure, and the like. Coupled with the scale on such a measuring device are numbers. Typically, a cardinal number system is used to indicate how many of the basic units of measure are realized at any point along the scale, the number indicating how many of the basic units of measure are between the given point and starting point, with a starting point usually labeled as zero.
It is simply not possible to accurately measure a distance without such a scale, because there is no reference to compare the distance to. Whether the comparison be made visually or otherwise, it is indeed possible to estimate the size of an object without the use of a scale, but such an estimate is made by comparison of the object with generally similarly sized object of roughly knowing measurement, and is therefore inherently inaccurate, at least to a degree. In order to measure an object accurately, direct comparison to a scale must be used.
As mentioned, one example of such a scale is simple rule that measure linear distances in centimeters, inches, or similar. Another common type of measurement is the measurement of angles. Angular scales of measurement are reasonably analogous to linear scales of measurement in that a set base measurement is used, with such a set base measurement being replicated in a contiguous manner to form an ongoing scale. In the case of angular measurement, the units of measurement are usually with reference to a circle, with a circle being divided into an equal number of divisions. Any two lines, surfaces, or the like, that intersect do so at an angle, with the angle being measurable in terms of these divisions of a circle. The most commonly used scale for measuring angles is a "degree" scale, wherein a circle is divided into 360 equal divisions, each division being named a "degree". An angle that is between two intersecting lines, or the like, wherein the angular displacement between the two lines, surfaces or the like is equivalent to one quarter of a circle, would have an angular measurement of 90.degree.. Under many circumstances, the direct measurement of such an angle is adequate and can be measured by an angular scale that indicates this measurement directly. Such an angular scale is commonly known as a protractor.
Many different kinds of protractors are commonly available. The most simple kind is one that is circular or semicircular and has no moving parts. An angular scale is part of the protractor, and the protractor is simply placed against a pair of intersecting lines, or the like, and the angle between such lines can be read directly from the angular scale on the protractor.
There are instances, however, where it is more useful to have an indicated measurement that is different than an actual measurement. The most simple example of this is the measurement of a drawing that is represented in a reduced scale. Using a ruler having a similarly reduced scale to measure the drawing gives a direct indication of the actual size of an object represented in the drawing, even though this is not the actual distance on the drawing. By this method, an object of any size can be represented in a more appropriate size, at a given scale. Such a procedure of using a reduced scale is often used in engineering drawings, architectural drawings, and the like.
Another example of a scale indicating a converted type of measurement is a simple speedometer on a car, wherein the displacement of a pointer along a scale, whether the scale be angular or linear, indicates the speed that the car is travelling at.
Such adjusted and adapted scales present useful information in a manner that is most convenient for the user. There is little or no conversion that is necessary in order to use the information gained from the scale.
It is believed that the conversion of angular scales is much less common than with linearly based scales. The fundamental reason behind this is that if a representation of an angle is made at an enlarged or reduced scale the actual angle remains unchanged. Resultingly, the same scale can be used to measure virtually any angle.
One possibility for requiring an altered angular scale, wherein the indicated angle may be different than the actual measured angle, is where some sort of mathematical computation would need to be performed on the actual measured angle in order to obtain a useful result. Such an example of this is the formation of a double bevelled corner, wherein two pieces of material are each cut at an angle that is equal to one half of the actual angle between the two pieces of material to be joined. If this angle is 90.degree., such as on a picture frame, each piece of material is cut at a 45.degree. angle. It is, of course, possible to measure the 90.degree. angle directly, and simply divide it by a factor of two in order to obtain the resulting angle of 45.degree.. It would be more convenient, however, to have a measuring instrument that actually indicates the required 45.degree. angle of cutting.
Another similar type of angle is a single bevelled angle, wherein in two pieces of material are joined together in a similar but slightly different manner than in a doubled bevelled angle. In a single bevelled angle, one piece of material is cut at end thereof at a desired angle--this angle being the same angle that the piece extending therefrom is to be directed at. The piece of material to be adjoined thereto contacts this bevelled surface along its side. In order to calculate the angle that a piece of material would be cut at for a single bevelled angle, the angle between two joining surfaces of the two pieces of material is measured. If the angle therebetween is acute, the complement of that angle is used. If the angle therebetween is obtuse, an angle that is 90.degree. less than the complement is used.